Range-finding and object-positioning systems and methods using same

ABSTRACT

A range-finding and/or object-positioning system comprises one or more target devices; one or more reference devices communicating with said one or more target devices via one or more wireless signal sets, each wireless signal set comprising at least a first-speed signal having a first transmission speed and a second-speed signal having a second transmission speed, and the first transmission speed being higher than the second transmission speed; and at least one processing unit performing actions for determining at least one distance between one target device and one reference device based on the time difference between the receiving time of the first-speed signal and the receiving time of the second-speed signal of the wireless signal set communicated between said reference and target devices.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/280,958, filed Jan. 20, 2016, the entirety ofwhich is incorporated herein by reference.

FIELD OF THE DISCLOSURE

The present invention relates generally to range-finding andobject-positioning methods and systems, and in particular to mixed moderange-finding and object-positioning systems and methods of finding thedistance between a reference object and a target object, and methods ofdetermining the position of an object using same.

BACKGROUND

Many types of rangefinders are known, for example, one type ofrangefinder generally comprises an infrared light emitting diode (LED)and a photodiode. The rangefinder emits an infrared pulse, which isreflected by a nearby object. The rangefinder receives the reflectedinfrared signal. Characteristics of the reflected infrared signal suchas intensity, time of flight, frequency and/or phase are then analyzedto derive the object's range.

Another type of known rangefinder is the common radar system. Anemitter, for example, a narrow beam width antenna such as a parabolicantenna, emits a radio frequency pulse (sometimes denoted as a signalbeam). Radio reflective materials of objects within the signal beamreflect the signal back to the emitter. Measurements of the reflectedsignal's time of flight and Doppler shift are then used to compute theobject's range, and in some systems, velocity.

Range-finding systems and methods, i.e., systems and methods fordetermining the distance between two objects, are often related toobject positioning systems and methods. For example, object positioningsystems usually use range-finding methods to first determine thedistance between a target object and each of one or more referenceobjects, and then determining the position of the target object.Examples of known object positioning systems include the GlobalPositioning System (GPS) of the United States, the Global NavigationSatellite System (GLONASS) of Russia, the Galileo positioning system ofthe European Union, and the BeiDou Navigation Satellite System of China.

A difficulty with these systems is that the propagation speed of theemitted radio frequency (RF) signal, which is substantially the speed oflight, is so high that even small errors in time of flight measurementamount to large errors in distance calculation, which results in morestringent and costly system requirements, e.g., precise timesynchronization, wide signal bandwidth, and the like.

SUMMARY

According to one aspect of this disclosure, there is provided a rangingapparatus. The ranging apparatus comprises: at least one signal receiverfor receiving at least one set of signals transmitted from at least onelocation, each of the at least one set of signals comprising at least afirst-speed signal having a first transmission speed and a second-speedsignal having a second transmission speed, and the first transmissionspeed being higher than the second transmission speed; and at least oneprocessing unit for determining the distance between the apparatus andeach of the at least one location based on the time difference betweenthe time of receiving the first-speed signal transmitted from saidlocation and the time of receiving the second-speed signal transmittedfrom said location.

In some embodiments, the distance between the apparatus and each of theat least one location is determined as:

${d = \frac{c_{1}c_{2}\Delta\; t}{c_{1} - c_{2}}},$wherein d is the distance between the apparatus and said location, Δt isthe time difference between the time of receiving the first-speed signaltransmitted from said location and the time of receiving thesecond-speed signal transmitted from said location, c₁ is the firstspeed, c₂ is the second speed, and c₁>c₂.

In some embodiments, the first-speed signal is a Radio Frequency (RF)signal, and the second-speed signal is an acoustic signal. An acousticsignal is a mechanical wave that propagates in a medium, such as a gas(e.g., air), liquid or solid as vibration, audio signal, sound,ultrasound (i.e., ultrasonic signal) and/or infrasound, whether audibleor inaudible. Hereinafter, the term “acoustic” and “audio” may be alsoused interchangeably for simplicity.

In some embodiments, the ranging apparatus further comprises atemperature sensor for determining the speed of sound for calibratingthe speed of the transmitted acoustic signal.

In some embodiments, the ranging apparatus further comprises atemperature sensor and a humidity sensor for determining the speed ofsound for calibrating the speed of the transmitted acoustic signal.

In some embodiments, the at least one signal receiver comprise at leasta first signal receiver for receiving the first-speed signal, and asecond signal receiver for receiving the second-speed signal.

In some embodiments, the first-speed signal and the second-speed signalof each signal set are substantially simultaneously transmitted from thefirst location.

According to one aspect of this disclosure, there is provided apositioning system. The positioning system comprises: one or more targetdevices; a plurality of reference devices communicating with said one ormore target devices via one or more wireless signal sets, each wirelesssignal set comprising at least a first-speed signal having a firsttransmission speed and a second-speed signal having a secondtransmission speed, and the first transmission speed being higher thanthe second transmission speed; and at least one processing unitperforming actions for determining at least one distance between onetarget device and one reference device based on the time differencebetween the receiving time of the first-speed signal and the receivingtime of the second-speed signal of the wireless signal set communicatedbetween said reference and target devices.

In some embodiments the at least one processing unit determines thelocation of one or more target devices using multilateration.

In some embodiments, the first-speed signal is a Radio Frequency (RF)signal, and the second-speed signal is an acoustic signal.

In some embodiments, the positioning apparatus further comprises atemperature sensor for determining the speed of sound for calibratingthe speed of the transmitted acoustic signal.

According to one aspect of this disclosure, there is provided aranging/positioning method. The method comprises: communicating, betweenone or more target devices and one or more reference devices, one ormore wireless signal sets, each wireless signal set comprising at leasta first-speed signal having a first transmission speed and asecond-speed signal having a second transmission speed, and the firsttransmission speed being higher than the second transmission speed; anddetermining at least one distance between one target device and onereference device based on the time difference between the receiving timeof the first-speed signal and the receiving time of the second-speedsignal of the wireless signal set communicated between said referenceand target devices.

According to one aspect of this disclosure, there is provided a virtualreality and/or augmented reality ranging/positioning system. The systemcomprises: communicating, between one or more target devices and one ormore reference devices, one or more wireless signal sets, each wirelesssignal set comprising at least a first-speed signal having a firsttransmission speed and a second-speed signal having a secondtransmission speed, and the first transmission speed being higher thanthe second transmission speed; and determining at least one distancebetween one target device and one reference device based on the timedifference between the receiving time of the first-speed signal and thereceiving time of the second-speed signal of the wireless signal setcommunicated between said reference and target devices.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram illustrating a ranging system having oneor more reference devices and one or more target devices in a site,according to one embodiment of the present disclosure;

FIG. 2 is a schematic diagram showing the determination of range betweena reference device and a target device of the system of FIG. 1;

FIGS. 3A and 3B show a flowchart illustrating the steps of measuringrange between the reference device and target device;

FIG. 4 shows an example of determining the distance between thereference device and target device, and the possible locations of thetarget device;

FIG. 5A shows an example of determining the location of the targetdevice from two reference devices and by using triangulation, while FIG.5B shows an example of determining the location of the target devicefrom two reference devices by using triangulation, wherein the targetdevice is collinear with the two reference devices;

FIG. 6 shows an example of determining the location of the target devicefrom three reference devices and by using triangulation;

FIG. 7A is a top view of a portion of the site of FIG. 1, showing threereference devices at known three-dimensional (3D) locations and a targetdevice, FIG. 7B is a side view of the site portion of FIG. 7A, and FIG.7C is a perspective view of the site portion of FIG. 7A;

FIG. 8 is a schematic diagram showing the determination of range betweena reference device and a target device of the system of FIG. 1,according to an alternative embodiment;

FIG. 9 illustrates a ranging system of FIG. 1 in the form of a 3D inputsystem, according to an alternative embodiment; and

FIG. 10A is a bottom view of a position sensing glove of the 3D inputsystem of FIG. 9, while FIG. 10B is a top view of the position sensingglove of FIG. 10A.

DETAILED DESCRIPTION

With reference to FIG. 1, a ranging system is shown and is generallyidentified by the reference numeral 100. As shown, the system 100comprises one or more reference devices 102 and one or more targetdevices 104 deployed in a site 106. The reference devices 102 in thisembodiment transmit a wireless signal set and the target devices 104receive the wireless signal set 108. Thus, the reference devices 102communicate with target devices 104 via the wireless signal set 108 fordetermining the ranges of the target devices 104. Herein, the range ofan object refers to at least the distance between the object and areference point, for example, a reference device.

In this embodiment, the one or more reference devices 102 are deployedat known locations of the site 106, for example, a device specificallydesigned for the purposes described herein, a WiFi® access point, aBluetooth® access point, and/or the like. As will be described in moredetail below, each reference device 102 also comprises a speaker.

The target devices 104 are associated with respective movable objects,such as humans, shopping carts, robots, a user's hands, and the like,moving within the site 106. The target devices 104 may be any devicehaving the functionality as described below and suitable for associatingwith movable objects, for example, signal-receiving devices specificallydesigned for the purposes described herein, smartphones such as Apple®iPhone®, Android™ phones, Windows® phones and other smartphones, tabletssuch as Apple® iPad®, Android™ tablet, Microsoft® tablet and othertablets, laptops, Personal Digital Assistant (PDA), video gamecontrollers, human-machine interface devices, three-dimensional (3D)interface devices for virtual reality applications, and the like.

The wireless signal set 108 transmitted between a reference device 102and a target device 104 comprises at least a first-type, high-speedwireless signal such as an RF signal, for example, a WiFi® signal, aBluetooth® signal, an Enhanced ShockBurst™ signal or the like, and asecond-type, low-speed wireless signal such as an acoustic signal.

As those skilled in the art appreciate, in various embodiments, areference device 102 may simultaneously communicate with one or moretarget devices 104, and a target device 104 may simultaneouslycommunicate with one or more reference devices 102. Of course, there mayexist, at least in some time one or more reference devices 102 that donot communicate with any target device 104, and there may also exist, atleast in some time periods, one or more target devices 104 that do notcommunicate with any reference device 102.

Suitable signal multiplexing technologies, such as frequency-divisionmultiplexing, time-division multiplexing, code-division multiplexing andthe like, may be used for communication between one or more referencedevices 102 and one or more target devices 104. As many of these signalmultiplexing technologies are known in the art, and as new signalmultiplexing technologies are equally applicable to the ranging systemdisclosed herein, the description in the following only uses onereference device 102 communicating with one target device 104 as anexample for illustrating the invention.

As shown in FIG. 2, a reference device 102 comprises a processing unit112A coupled to and controlling, via a bus or individual circuitries(not shown), a memory component 114A, and a set of signal transmittersincluding an RF transceiver 116A, and an acoustic transmitter 120A. TheRF transceiver 116A is coupled to an antenna 118A for communicating withthe target device 104 via a high-speed wireless signal such as an RFsignal 124. As is known in the art, an RF transceiver is capable oftransmitting and receiving an RF signal.

The acoustic transmitter 120A is coupled to a speaker 122A fortransmitting a low-speed wireless signal such as an acoustic signal 126.In this embodiment, the acoustic transmitter 120A is a digital to analogconverter (DAC), generating an analog signal to drive the speaker 122Aand to produce the low-speed wireless signal 126.

In various embodiments, the reference device 102 may further compriseother suitable components and circuitry, depending on theimplementation. For example, in some embodiments, the reference device102 may comprise suitable signal-processing components and circuitry forprocessing the RF and/or acoustic signals for transmission. In anotherexample, the reference device 102 may comprise suitablesignal-processing components and circuitry for filtering the output ofthe DAC 120A.

From a functionality point of view, the processing unit 112A is alsodenoted as the transmitter logic layer. The RF transceiver 116A, antenna118A, acoustic transmitter 120A and speaker 122A are collectivelydenoted as the transmitter physical layer.

Correspondingly, the target device 104 comprises a processing unit 112Bcoupled to and controlling, via a bus or individual circuitries (notshown), a memory component 114B, and a set of signal receivers includingan RF transceiver 116B, and an acoustic receiver 120B. The RFtransceiver 116B is also coupled to an antenna 118B for communicatingwith the reference device 102 via the RF (wireless) connection 124(i.e., the RF signal 124; hereinafter the terms “RF signal” and “RFconnection” may be also used interchangeably for simplicity). Theacoustic receiver 120B is also coupled to a microphone 122B forreceiving the acoustic signal transmitted from the reference device 102.In this embodiment, the acoustic receiver 120B is an analog to digitalconverter (ADC), converting the output of the microphone 122B to adigital signal for further processing. In some embodiments, the targetdevice 104 further comprises a temperature sensor 132.

From a functionality point of view, the processing unit 112B is alsodenoted as the receiver logic layer. The RF transceiver 116B, antenna118B, acoustic receiver 120B and microphone 122B are collectivelydenoted as the receiver physical layer.

Herein, each of the processing units 112A and 112B may be a speciallydesigned controller chip using for example a programmedfield-programmable gate array (FPGA), an application-specific integratedcircuit (ASIC), and/or the like. Alternatively, each of the processingunits 112A and 112B may be one or more single-core or multiple-corecomputing processors, such as Intel® microprocessors offered by IntelCorporation of Santa Clara, Calif., USA, AMD® microprocessors offered byAdvanced Micro Devices of Sunnyvale, Calif., USA, ARM® microprocessorsmanufactured by a variety of manufactures under the ARM® architecturedeveloped by ARM Ltd. of Cambridge, UK, AVR® microcontrollers offered byAtmel® corporation of San Jose, Calif., USA, and/or the like. Each ofthe memory components 114A and 114B may be RAM, ROM, EEPROM, solid-statememory, hard disks, CD, DVD, flash memory, and/or the like.

The reference device 102 and the target device 104 use an RF signal 124and an acoustic signal 126 for measurement of the range 128therebetween. In this embodiment, the reference device 102 and thetarget device 104 also use the RF connection 124 for other communicationpurposes, such as sending and receiving commands and data to/from eachother. However, those skilled in the art appreciate that, in somealternative embodiments, the RF connection 124 shown in FIG. 2 is usedfor range measuring only, and the reference device 102 and the targetdevice 104 do not communicate with each other for other purposes. Insome other embodiments, the RF connection 124 shown in FIG. 2 is usedfor range measuring only, and the reference device 102 and the targetdevice 104 use a different wireless means, e.g., a different wirelesschannel, a different wireless communication technology, forcommunicating with each other for other purposes such as sending andreceiving commands and data to/from each other. As an example, in oneembodiment, the reference device 102 and the target device 104 use a anEnhanced ShockBurst™ signal as the RF signal 124 for range measuring,and use a Bluetooth® connection for sending and receiving commands anddata to/from each other.

FIG. 3A is a flowchart showing the steps of measuring range between thereference device 102 and target device 104. As shown, a rangemeasurement may be initiated by an initiator from the reference deviceside (step 202), or from the target device side (step 204). Theinitiator may be a user who manually initiates the range measurement by,for example, pressing a button on the reference device 102 or on thetarget device 104.

Alternatively, the initiator may be a computer program or service, whichautomatically initiates the range measurement as needed or periodicallyat predefined time intervals. The computer program or service may be aprogram or service running in the reference device 102 or the targetdevice 104, or may be a program or service running in an external devicein communication with the reference device 102 or the target device 104.For example, a user-launched map or navigation program running on thetarget device 104 may automatically and periodically request rangemeasurement for updating the position of the target device 104. Asanother example, an external service such as a shopping cart trackingservice running on an external server may communicate with one or morereference devices 102, requesting range measurement of the targetdevices 102 installed on shopping carts to continuously track theshopping carts in the site 106.

Further, the computer program or service may comprise software codestored in a content-erasable memory such as a hard drive, a solid-statememory, and/or the like. Alternatively, the computer program or servicemay comprise firmware code stored in a ROM, an EPROM (the content ofwhich may be erasable using a special programming method), and/or thelike.

If the range measurement request is initiated from the reference deviceside, the reference device 102 initiates the range measurement processat step 210.

On the other hand, if the range measurement request is initiated fromthe target device side, the target device 104 sends the request to thereference device 102, requesting the reference device 102 to begin therange measurement process (step 208). On the reference device side, inresponse to the range measurement request, the reference device 102initiates the range measurement process (step 210).

After initiating range measurement, the reference device 102 transmitsan RF signal 124 and an acoustic signal 126 to the target device 104,respectively, via the RF transceiver 116A through the antenna 118A, andvia the acoustic transmitter 120A through the speaker 122A (steps 212and 214, respectively).

In this embodiment, the low-speed acoustic signal 126 at the transmitterside is encoded with a binary codeword of length L_(P), denoted byP_(AC)[n],and then modulated to a ultrasonic frequency for transmission.As will be described in more detail later, at the receiver side, thereceived acoustic signal is demodulated and the decoded for furtherprocessing. Those skilled in the art appreciate that, in variousembodiments, either, both, or neither of the RF and acoustic signals 124and 126 may be encoded using a suitable coding scheme. Those skilled inthe art appreciate that a variety of binary/M-ary coding schemes, forexample, those using pseudorandom noise code, Gold code, Barker code, orthe like, may be used for encoding the RF signal 124 and/or the acousticsignal 126. Coding is commonly used in positioning for improved time ofarrival estimation, error detection, error correction, interferencecombatting and/or the like. Codeword modulation (inclusion) may be doneusing a variety of modulation methods e.g. on-off keying (OOK), audiofrequency shift keying (AFSK), Binary Frequency Shift Keying (BFSK),Amplitude Shift Keying (ASK), Continuous Phase Frequency Shift Keying(CPFSK), or the like.

Preferably, the high-speed, RF signal 124 and the low-speed, acousticsignal 126 are transmitted substantially simultaneously. The RF andacoustic signals 124 and 126 propagate through their respective media.The speed of the RF signal 124 in air is approximately the speed oflight, which is about 2.99×10⁸ meters per second (m/s) in free space. Onthe other hand, the speed of the acoustic signal 126 is the speed ofsound, which is approximately 343.4 m/s in air at 20° C.

At the target device, the target device 104 receives the RF signal 124via the antenna 118B and the RF transceiver 116B, and stores thereceived RF signal and the time-of-arrival t_(RF) of the received RFsignal 124, in the memory component 1146 (step 218).

As the speed of the acoustic signal 126 is influenced by environmentalfactors, primarily temperature, upon receipt of the RF signal 124, thetarget device 104 uses the temperature sensor 132 (see FIG. 2) tomeasure the ambient air temperature T_(s) (step 220), and calculates alocalized acoustic signal speed v_(AC) asv _(AC)≈331.4+0.6T _(s),  (1)where T_(s) is in degrees Celsius. Of course, in various embodiments,the localized acoustic signal speed v_(AC) may be calculated withmultiple measurements over time, filtered, and/or by using other knownmethods, such as Newton-Laplace equations, etc.

Then, the target device 104 starts to receive the acoustic signal 126from the microphone 122B, storing the samples and the sampling startingtime in memory 114B (step 224).

In this embodiment, receiving the acoustic signal 126 is conducted bysampling the output of the microphone 122B via the analog-to-digitalconverter 120B. After sampling, at step 222, the acoustic signal 126,represented in the discrete time domain and herein denoted as S_(A)[n],and the time at which the sampling of the acoustic signal began, i.e.,the starting time t_(SA) of step 222, are stored in the memory component114B (step 224).

After a period of time corresponding to a maximum time-of-flight t_(max)expected for a predefined maximum observable range d_(max), the acousticsignal sampling is stopped, and the process enters step 226. In thisexample, the acoustic signal 126, and therefore the discrete-timeacoustic signal S_(A)[n], comprises the codeword P_(AC)[n].

A simplified approximation of the relationship between t_(max) andd_(max) is t_(max)=(d_(max)/v_(AC))+δ, although a more accurate equationthat derives from (6) may also be used, The variable ‘δ’ is a predefineddesign parameter. For example, in some embodiments, where a binarycodeword P_(AC)[n] of length L_(p) (bits) is used, any valueδ<L_(p)T_(b), where T_(b) is the length of one bit of the codewordP_(AC)[n] in seconds, results in the truncation of the acoustic signal126, affecting signal-to-noise ratio (SNR), hence, impacting theaccuracy of range estimation. For simplicity of operation and withoutany loss of generality in the embodiments disclosed herein, it ispredefined that δ=0.

In some embodiments, the time at which the sampling of the acousticsignal begins relative to the time-of-arrival of the high-speed signalt_(RF) may be delayed by a fixed or determined value,τ_(SA)=t_(SA)−t_(RF), and the period of time the acoustic signal issampled is a fixed or determined window period t_(WIN), i.e.,d _(max) =v _(AC)(τ_(SA) +t _(WIN)),

This implies a minimum observable distance d_(min) given asd _(min)=τ_(SA) v _(AC)

In some embodiments, τ_(SA) and t_(WIN) may be determined from previousdetermined distances.

At step 226, the target device 104 then processes the received RF andacoustic signals 124 and 126 to calculate the time difference Δt betweenthe time-of-arrivals t_(RF) and t_(AC), i.e., Δt=t_(AC)−t_(RF). Here,t_(AC) is the time of arrival of the received acoustic signal 126. Atthis step, the time-of-arrival of each signal 124, 126 is determinedusing suitable signal processing methods depending on theimplementation. For example, FIG. 3B illustrates an example of thedetailed steps for calculating the time difference Δt in discrete-timedomain.

As shown in FIG. 3B, at step 252, a bandpass filter (BPF) is applied tothe received acoustic signal S_(A)[n] for noise reduction, generating afiltered acoustic signal S_(F)[n]. Note that the received acousticsignal S_(A)[n] generally comprises noise, and may be distorted, forexample, may exhibit a frequency shift from the transmitted acousticsignal. The BPF bandwidth is set to be wider than the acoustic signalbandwidth to account for sources of frequency shift, such as oscillatoroffset between the target device 104 and the reference device 102,Doppler shift due to relative motion, and the like.

While in this embodiment, the acoustic signal is first sampled, and thenthe sampled acoustic signal is bandpass filtered, in some alternativeembodiments, the acoustic signal may first be bandpass filtered, and thefiltered acoustic signal is sampled to obtain the filtered acousticsignal S_(F)[n]. In some other embodiments, bandpass filtering may beomitted.

Still referring to FIG. 3B, in this embodiment, the acoustic signalS_(F)[n] is demodulated at step 254. Those skilled in the art appreciatethat the demodulation process varies depending on the implementation andmay include frequency estimation (e.g. using FFT or other frequencyestimation methods), down conversion, filtering (e.g. low-passfiltering), and the like. The outcome of signal demodulation at step 253is a demodulated signal S_(d)[n], which in this embodiment contains thecodeword P_(AC)[n].

At step 256, a local replica signal S_(L)[n] is generated at the targetdevice 104, having the same codeword, P_(AC)[n] as the acoustic signal126 at the transmitter side before modulation.

In some embodiments, the local replica signal S_(L)[n] is generated suchthat it also accounts for the estimated oscillator offset between thereference device 102 and the target device 104, and/or other sources offrequency shift, e.g. Doppler shift, and the like, by scaling thesample-rate at which the local signal is generated.

At step 258, the local replica signal S_(L)[n] is cross-correlated withthe demodulated signal S_(d)[n] as follows:

$\begin{matrix}{{{R\left\lbrack n_{d} \right\rbrack} = {\sum\limits_{n = 1}^{N}{{S_{L}\left\lbrack {n - n_{d}} \right\rbrack}{S_{d}\lbrack n\rbrack}}}},} & (2)\end{matrix}$where N is the total number of samples in the signal S_(d)[n]. Then, atstep 260, the offset n₀ between the local replica signal S_(L)[n] andthe demodulated acoustic signal S_(d)[n] is estimated using suitabletime of arrival estimation methods. For example, in this embodiment, aMaximum Likelihood estimator is used to estimate the offset n₀ as:

$\begin{matrix}{{{\sum\limits_{n = 1}^{N}{{S_{L}\left\lbrack {n - n_{0}} \right\rbrack}{S_{d}\lbrack n\rbrack}}} = {\max\limits_{n_{d}}\left( {R\left\lbrack n_{d} \right\rbrack} \right)}},} & (3) \\{n_{0} = {{\underset{n_{d}}{argmax}\left( {R\left\lbrack n_{d} \right\rbrack} \right)}.}} & (4)\end{matrix}$

As in this embodiment a correlator is used, n₀ thus represents theoffset in samples between S_(L)[n] and S_(d)[n]. Thus, at step 262, thetime difference Δt between the time-of-arrivals t_(RF) and t_(AC) in thecontinuous-time domain is:

$\begin{matrix}{{\Delta\; t} = {{t_{AC} - t_{RF}} = {t_{SA} + \frac{n_{0}}{F_{s}} - t_{RF}}}} & (5)\end{matrix}$where F_(s) is the sampling rate (in samples per second) of theanalog-to-digital converter 120B, and thus is the sampling rate of thereceived acoustic signal 126. The process then goes to step 228 of FIG.3A.

In some alternate embodiments, interpolation methods may be used toimprove the estimation accuracy of t_(AC). The standard parabolicinterpolation method is given below, however other methods are known andmay be used, such as the early-late method.

$t_{AC} = {t_{SA} + {\frac{1}{F_{s}}\left\lbrack {n_{0} + \frac{\left( {{R\left\lbrack {n_{0} + 1} \right\rbrack} - {R\left\lbrack {n_{0} - 1} \right\rbrack}} \right)}{2\left( {{2{R\left\lbrack n_{0} \right\rbrack}} - {R\left\lbrack {n_{0} - 1} \right\rbrack} - {R\left\lbrack {n_{0} + 1} \right\rbrack}} \right)}} \right\rbrack}}$

Referring again to FIG. 3A, at step 228, the target device 104calculates the range or distance d between the reference device 102 andthe target device 104 as:

$\begin{matrix}{{d = \frac{v_{RF}v_{AC}\Delta\; t}{v_{RF} - v_{AC}}},} & (6)\end{matrix}$where v_(RF)=2.99×10⁸ m/s is the RF signal speed, v_(AC) is thelocalized acoustic signal speed calculated using Equation (1), and Δt iscalculated using Equation (5).

The calculated range d is further processed (step 230). For example, ifthe target device 104 is not the initiator of the measurement, then thecalculated range d may be reported to the initiator. As another example,in alternative embodiments where the target device 104 is not theinitiator of the measurement, then it may report one or more of themeasured/calculated/estimated parameters e.g., Δt, t_(AC), thecalculated range d, and/or other relevant parameters, to the initiator.

In some embodiments, some of the target devices 104 are equipped withother ancillary sensors e.g. accelerometer, gyroscope, infrared sensor,and/or the like. The inclusion of such ancillary sensor(s) provide(s)additional information about other environmental parameters and/or aboutthe state of the device, e.g., its orientation, which may be deemeduseful for some applications such as virtual reality for example.

In some embodiments, the reference device 102 and the target device 104are substantially at the same elevation. Then, as shown in FIG. 4, aftercalculation of d, it is determined that the target device 104 is locatedat a point on the circle 282 centered at the reference device 102 andhaving a radius of about d. As the reference device 102 is at a knownlocation in the site 106, the location of the target device 104 is thensomewhere along the circle perimeter 282. In some embodiments that theaccurate location of the target device 104 is not required, determiningthe location of the target device 104 to be somewhere along theperimeter of a calculated circle may be sufficient.

As shown in FIG. 5A, in some embodiments, the range measurement shown inFIGS. 3A and 3B is conducted for determining the distance between thetarget device 104 and each of two reference devices 102A and 102B,wherein the distance D between reference devices 102A and 102B is known.Following the process 200 of FIGS. 3A and 3B target device, it isestimated that the distance between the reference device 102A and thetarget device 104 is d₁, and the distance between the reference device102B and the target device 104 is d₂. In this example, it is furtherassumed that the reference devices 102A and 102B and the target device104 are substantially at the same elevation. Then, the location of thetarget device 104 may be determined using well-known triangulation atany one of the two locations 104-1 and 104-2. In some embodiments thatthe accurate location of the target device 104 is not required,determining the location of the target device 104 to be at one of twopossible locations may be sufficient.

As shown in FIG. 5B, in some embodiments where a target device 104 iscollinear with two reference devices 102, after determining the distancebetween the target device 104 and each of the two reference devices 102,the position of the target device 104 may be determined as aone-dimensional (1D) position along the line of the two referencedevices 102 based on the determined distances between the target device104 and the two reference devices 102.

In some other embodiments, the system may use other suitable informationto refine the location of the target device. For example, if the systemknows that the target device 104 can only be located on one side of theline connecting the reference devices 102A and 102B, for example, theother side is an area or room inaccessible to the target device 104,then, the system can further refine the location of the target device104 to be one of the locations 104-1 and 104-2 that is accessiblethereto.

In another embodiment as shown in FIG. 6, three reference devices 102A,102B and 102C may be used for determining the location of a targetdevice 104 to be within the area 104-3, after calculating the distancesd₁, d₂, and d₃ between between the target device 104 and the referencedevices 102A, 102B and 102C, respectively. In this embodiment, thesystem assumes that the target device 104 and the three referencedevices 102A, 102B and 102C are at the same elevation.

In an alternative embodiment, the system does not consider that thetarget device 104 and reference devices 102 are at the same elevation.For example, FIGS. 7A to 7C show three reference devices 102A, 102B and102C at the same elevation 302, and a target device 104 not necessarilyat the same elevation as the reference device 102A to 102C. Thedistances r₀ between reference devices 102A and 102B, r₁ betweenreference devices 102A and 102C and r₂ between reference devices 102Band 102C, are known.

In this example, a local right-handed coordinate system is defined (asshown in FIG. 7C) with the reference device 102A at the center (i.e.x_(a)=0, y_(a)=0, z_(a)=0). It is further assumed that the referencedevice 102B is located on the positive x-axis (i.e., x_(b)=r₀>0,y_(b)=0) and the reference device 102C is located on the first or thesecond quadrant on the x-y plane of the coordinate system excluding onthe x-axis (i.e. y_(c)>0). With these assumptions, the location of thereference device 102C, (x_(c), y_(c), z_(c)), relative to thiscoordinate system may be calculated from the well-known trilaterationequations as:

$\begin{matrix}{{x_{c} = \frac{r_{0}^{2} + r_{1}^{2} - r_{2}^{2}}{2r_{0}}},} & (7) \\{{y_{c} = \sqrt{r_{1}^{2} - \left( \frac{r_{0}^{2} + r_{1}^{2} - r_{2}^{2}}{2r_{0}} \right)^{2}}},} & (8) \\{z_{c} = 0.} & (9)\end{matrix}$

Following the process 200 of FIGS. 3A and 3B, the distances u₀, u₁ andu₂ between the target device 104 and, respectively, the referencedevices 102A, 102B and 102C are determined. Then, using the well-knowntrilateration equations, the location of the target device 104 relativeto the coordinate system defined earlier target device may be calculatedas:

$\begin{matrix}{{x_{m} = \frac{u_{0}^{2} - u_{1}^{2} + r_{0}^{2}}{2r_{0}}},} & (10) \\{{y_{m} = {\frac{u_{0}^{2} - u_{2}^{2} + x_{c}^{2} + y_{c}^{2}}{2y_{c}} - {\frac{x_{c}}{y_{c}}x_{m}}}},} & (11) \\{{{z_{m} = {z_{m}^{+} = \sqrt{u_{0}^{2} - x_{m}^{2} - y_{m}^{2}}}},{or}}{z_{m} = {z_{m}^{-} = {- \sqrt{u_{0}^{2} - x_{m}^{2} - y_{m}^{2}}}}}} & (12)\end{matrix}$Therefore, the location of the target device 104 may be at (x_(m),y_(m), z_(m) ⁺), or at (x_(m), y_(m), z_(m) ⁻). In some embodiments thatthe accurate location of the target device 104 is not required,determining the location of the target device 104 to be at any one oftwo possible locations may be sufficient. In some embodiments,determining the target device 104 is at any one of two possiblelocations may be sufficient for relative positioning thereafter.

In some embodiments, the system may further use other suitableinformation to refine the location of the target device 104. Forexample, if the location (x_(m), y_(m), z_(m) ⁻) is inaccessible to thetarget device, or if the system knows that the references devices are ona floor of a room, and the target device 104 is on or above the floor302, the system then determines that the location of the target deviceis at (x_(m), y_(m), z_(m) ⁺). Alternatively, the system may use morethan three non-coplanar reference devices 102 to more accuratelydetermine the location of the target device 104.

For the marginal case in which the reference devices 102 are coplanar,the location of the target device calculated using trilateration, ormore generally, multilateration, may be ambiguous, and the system mayfurther use other suitable information, e.g., the area accessibility orinaccessibility of the target device 104 to eliminate unlikely locationsand solve the ambiguity.

Other suitable position estimate methods can alternatively be used. Forexample, in one embodiment, a Least Squares method may be used tocalculate the 3D coordinates (x_(m), y_(m), z_(m)) of the target device104 in the 3D space using the known positions (x₁, y₁, z₁), (x₂, y₂,z₂), . . . , (x_(N), y_(N), z_(N)) of four or more reference devices102, relative to an arbitrary but otherwise known coordinate system. Inthis example, it is further assumed that at least one of the referencedevices 102 is non-coplanar relative to other reference devices 102.Following the process 200 of FIGS. 3A and 3B the distances R₁, R₂, . . ., and R_(N) between the target device 104 and the N reference devices102 are determined as:R _(n)=(x _(m) −x _(n))²+(y _(m) −y _(n))²+(z _(m) −z _(n))²,  (13)for n=1, 2, . . . , N.

Define

$\begin{matrix}{{P = \begin{bmatrix}x_{1} \\y_{1} \\z_{1} \\\vdots \\x_{N} \\y_{N} \\z_{N}\end{bmatrix}},} & (14) \\{{P_{m} = \begin{bmatrix}x_{m} \\y_{m} \\z_{m}\end{bmatrix}},} & (15) \\{and} & \; \\{R = {\begin{bmatrix}R_{1} \\\vdots \\R_{N}\end{bmatrix}.}} & (16)\end{matrix}$

Then, the location of the target device 104 relative to the referencedevices with respect to the defined coordinate system can be expressedas:

$\begin{matrix}{{\begin{bmatrix}x_{m} \\y_{m} \\z_{m} \\\sqrt{x_{m}^{2} + y_{m}^{2} + z_{m}^{2}}\end{bmatrix} = {\left( {A^{T}A} \right)^{- 1}A^{T}b}},} & (17)\end{matrix}$where (⋅)^(T) represents matrix transpose, (⋅)⁻¹ represents matrixinverse,

$\begin{matrix}{{A = \begin{bmatrix}{{- 2}x_{1}} & {{- 2}y_{1}} & {{- 2}z_{1}} & 1 \\{{- 2}x_{2}} & {{- 2}y_{2}} & {{- 2}z_{2}} & 1 \\\vdots & \vdots & \vdots & \vdots \\{{- 2}x_{N}} & {{- 2}y_{N}} & {{- 2}z_{N}} & 1\end{bmatrix}},} & (18) \\{and} & \; \\{b = {\begin{bmatrix}{R_{1} - x_{1}^{2} - y_{1}^{2} - z_{1}^{2}} \\\vdots \\{R_{N} - x_{N}^{2} - y_{N}^{2} - z_{N}^{2}}\end{bmatrix}.}} & (19)\end{matrix}$

In some embodiments, the positions of all or a subset of the referencedevices 102 may be surveyed during calibration.

Those skilled in the art appreciate that latency in the reference andtarget devices 102 and 104 may cause error in range determination.Herein, the latency comprises audio latency, i.e., the latency of theaudio signal 126, and RF signal latency, i.e., the latency of the RFsignal 124.

The audio latency in the reference device 102 refers to the delay ortime difference from the time that the processing unit 112A signals thedigital to analog converter 120A to transmit the audio signal 126, tothe time that the audio signal 126 has actually been transmitted fromthe speaker 122A. The RF signal latency in the reference device 102refers to the delay from the time that the processing unit 112A signalsthe RF transceiver 116A to transmit the RF signal 124, to the start oftransmission of the RF signal 124 from the antenna 118A.

Similarly, the audio latency in the target device 104 refers to thedelay from the time that the audio signal 126 is received by themicrophone 122B, and the time that the received audio signal 126 hasbeen received by the processing unit 1126 for processing. The RF signallatency in the target device 104 refers to the delay from the time thatthe RF signal 124 is received at the antenna 118B, and the time that thereceived RF signal 124 has been time-tagged by the transceiver.

In some embodiments, the overall latency is considered small and henceignored. However, in these embodiments, the accuracy of the calculateddistance, and consequently the accuracy of the calculated target devicelocation may be reduced.

In some embodiments, the system estimates the overall latency using acalibration process to improve the rangefinding and/or objectpositioning accuracy.

In an alternate embodiment, an arbitrary but known delay τ^(−ENC) isintroduced in the transmission of the acoustic signal 124, for example,for privacy/security purposes. Therefore, calculation of the correctrange requires specific knowledge of the additional term τ^(−ENC).Depending on the implementation, τ^(−ENC) may be generated from apre-shared key such as with a HMAC-based one-time password (HOTP)algorithm, time-based one-time password (TOTP) algorithm or the like, orpre-generated by a central server, or generated randomly andcommunicated to the receiver using public key cryptographic methods,such as RSA or the like.

In an alternative embodiment, some reference devices 102 may eachcomprise an RF signal transmitter rather than an RF transceiver. Thesereference devices 102 therefore can only act as signal transmitters.

In an alternative embodiment, some target devices 104 may each comprisean RF signal receiver rather than an RF transceiver. These targetdevices 104 therefore can only receive RF signals.

In an alternative embodiment as shown in FIG. 8, some reference devices102 may each comprise a temperature sensor 132A. In this embodiment, thespeed of sound is also calculated at the reference devices 102, and anaveraged speed of sound is calculated by averaging the calculated speedsof sound at both the reference devices 102 and the target device 104 forimproved accuracy.

In an alternative embodiment, the high-speed wireless signal 124 is anoptical signal. A disadvantage of the system in this embodiment is thatobstacles may block the optical signal path, therefore hindering therange estimation.

In above embodiments, temperature sensor is used for calibrating thespeed of sound. In some alternative embodiments, other known methods maybe used to measure the local speed of sound or the ambient temperature.

In some alternative embodiments, neither the target device 104 nor thereference device 102 contains a temperature sensor. In this embodiment,an approximate predefined value may be used. Those skilled in the artappreciate that ranging errors may result from such approximation.

In some embodiments, the high-speed, RF signal 124 and the low-speed,acoustic signal 126 are transmitted substantially simultaneously orwithin a time interval as small as possible. In an alternativeembodiment, one of the RF signal 124 and the acoustic signal 126 istransmitted at a different time instant after the transmission of theother thereof, with a predefined time delay that is known to theinitiating device.

In some embodiments, the reference devices 102 transmit the wirelesssignal set 108, and the target devices receive the wireless signal set108. In some alternative embodiments, the target devices 104 maytransmit the wireless signal set 108, and the reference devices 102 mayreceive the wireless signal set 108.

For example, as shown in FIG. 9, in some alternative embodiments, thepositioning system 100 may be part of a virtual reality (VR) systemand/or augmented reality (AR) system.

In the example of FIG. 9, the virtual reality (VR) system is athree-dimensional (3D) input system. The 3D input system 100 comprises acomputing device (not shown) such as a tablet, smartphone, laptopcomputer, desktop or the like, one or more wearable devices such asgloves 500 each coupled with a target device 104 (see FIGS. 10A and10B), and a plurality of reference devices 102 at known locations. Thecomputing device is in communication with the gloves 500 and thereference devices 102 using a suitable wireless connection, e.g. ANT®,Bluetooth®, or the like, enabling a variety of user inputs, e.g. variousgestures or commands. Other wireless or wired communication methods,e.g., WiFi®, ZigBee®, Ethernet, USB, Optical connection, serial cable,parallel cable, or the like, may alternatively be used for functionallyconnecting the computing device, the gloves 500 and the referencedevices 102.

FIGS. 10A and 10B show the bottom (palm) and top (back) views of aright-hand position sensing glove 500, respectively. A left-handposition sensing glove is similar to that of FIGS. 15A and 15B but witha generally mirrored configuration. The glove 500 is made of lightweightfabrics and mesh so as to minimize hindering the user's dexterity. Asshown, the glove 500 comprises five finger portions 504 to 512 and awrist portion 514, corresponding to the five fingers and the wrist ofthe user's hand. A plurality of angle encoders 520 are installed on thetop side of the glove 500 at the positions corresponding to the jointsof human fingers (i.e., on the joints of the entire finger from thefingertip to the knuckle of the finger joining the hand) for detectingthe angle of the respective joint. An angle encoders 522 is alsoinstalled on the glove 500 at the wrist position 514 for detecting theangle of the wrist. A target device 104 is affixed to the glove 500 toprovide ranging information of the glove 500 relative to one or morereference devices 102. The ranging information may then be fused withthe measured angles detected by the angle encoders on the glove 500 tointerpret a variety of user inputs such as hand gesture or commands in a3D space. The 3D input system 100 and the position sensing glove 500 aresimilar to those described in US Patent Publication No. US 2016/0132111A1, published on May 12, 2016 and assigned to the Applicant of thesubject application, the content of which is incorporated herein byreference in its entirety.

After determining the 3D position of the glove 500, the position of eachfingertip in the 3D space may be determined. Gestures and/or commandscan then be determined based on the obtained positions.

Other VR equipment may also comprise one or more target devices 104 fordetermining the range/position thereof in a 3D space. For example, insome embodiments, a head-mounted display may comprise a target device104 affixed thereto for range estimation or relative position estimationwithin the virtual environment.

Those skilled it the art appreciate that it is not necessary that allreference devices have to be transmitter devices for transmittingwireless signal sets and all target devices have to be receiver devicesfor receiving wireless signal sets, nor that all target devices have tobe transmitter devices and all references devices have to be receiverdevices. In fact, in some embodiments, some references devices may betransmitter devices and other references devices may be receiverdevices. Correspondingly, some target devices may be receiver devicesand other target devices may be transmitter devices.

Although embodiments have been described above with reference to theaccompanying drawings, those of skill in the art will appreciate thatvariations and modifications may be made without departing from thescope thereof as defined by the appended claims.

What is claimed is:
 1. An apparatus comprising: at least one signalreceiver for transmitting or receiving at least one set of signals to orfrom at least one location, each of the at least one set of signalscomprising at least a Radio Frequency (RF) signal and an acousticsignal; a temperature sensor; and at least one processing unit coupledto the at least one signal receiver and the temperature sensor for:calculating a first temperature-adjusted speed of sound by using thetemperature measurement obtained by the temperature sensor; calculatinga calibrated speed of the acoustic signal by averaging the first speedof sound and at least one second temperature-adjusted speed of sound atthe at least one location; and determining the distance between theapparatus and each of the at least one location based on the timedifference between the time of receiving the RF signal transmitted fromsaid location and the time of receiving the acoustic signal transmittedfrom said location.
 2. The apparatus of claim 1 wherein the at least oneprocessing unit is configured for determining the distance between theapparatus and each of the at least one location comprises calculatingsaid distance as: ${d = \frac{c_{1}c_{2}\Delta\; t}{c_{1} - c_{2}}},$${{\Delta\; t} = {t_{SA} + \frac{n_{0}}{F_{s}} - t_{RF}}},$ wherein d isthe distance between the apparatus and said location, Δt is the timedifference between the time of receiving the RF signal transmitted fromsaid location and the time of receiving the acoustic signal transmittedfrom said location, c₁ is the speed of the RF signal, c₂ is the speed ofthe acoustic signal and c₁ >c₂, t_(SA) is the time at which sampling ofthe acoustic signal began, F_(s), is the sampling rate of sampling thereceived acoustic signal, and t_(RF) is the time-of-arrival of thefirst-speed signal, and n₀ is an estimated offset between thetime-of-arrival of the acoustic signal and t_(SA).
 3. The apparatus ofclaim 1 wherein the at least one signal receiver comprises at least afirst signal receiver for receiving the RF signal, and a second signalreceiver for receiving the acoustic signal.
 4. The apparatus of claim 1wherein the RF signal and the acoustic signal of each signal set aresimultaneously transmitted from the first location.
 5. The apparatus ofclaim 1 wherein at least one of the RF signal and the acoustic signal isencoded.
 6. The apparatus of claim 1 wherein the at least one signalreceiver is configured for receiving at least three signal setstransmitted from at least three locations; and wherein the at least oneprocessing unit is configured for, after determining the distancebetween the signal receiver and each of the at least three locations,determining the position of the signal receiver in a three-dimensional(3D) space with respect to the at least three locations to be any one oftwo possible positions, said two possible positions being calculated byusing trilateration based on the distances between the apparatus and theat least three locations.
 7. The apparatus of claim 6 wherein the atleast one processing unit is further configured for determining theposition of the apparatus from the two possible positions based on anaccessibility of the apparatus to each of the two possible positions. 8.The apparatus of claim 1 wherein the at least one signal receiver isconfigured for receiving the signal sets transmitted from a plurality oflocations; and wherein the at least one processing unit is configuredfor, after determining the distance between the apparatus and each ofthe at least three locations, determining the location of the apparatusin a 3D space by using a Least Squares method based on the determineddistances between the apparatus and the at least three locations, andthe coordinates of each of the a plurality of locations in the 3D space.9. The apparatus of claim 2 wherein the at least one processing unitcomprises a Maximum Likelihood estimator for estimating n₀.
 10. Apositioning system comprising: a plurality of reference devices having acoordinate system associated therewith, at least one of the plurality ofreference devices located at an unknown position in said coordinatesystem; one or more target devices at unknown positions in saidcoordinate system, said one or more target devices in communication withthe plurality of reference devices via one or more wireless signal sets,each wireless signal set comprising at least a first-speed signal havinga first transmission speed and a second-speed signal having a secondtransmission speed, and the first transmission speed being higher thanthe second transmission speed; and at least one processing unitconfigured for: calculating the position of the reference device whoseposition is unknown in said coordinate system based on the distancesbetween the plurality of reference devices; and for each target device,determining the distance between the target device and each of theplurality of reference devices based on the time difference between thereceiving time of the first-speed signal and the receiving time of thesecond-speed signal of the wireless signal set communicated between saidreference and target devices; and determining the position of saidtarget device in said coordinate system based on the determineddistances.
 11. The positioning apparatus of claim 10 wherein thefirst-speed signal is a Radio Frequency (RF) signal, and thesecond-speed signal is an acoustic signal.
 12. A positioning methodcomprising: communicating one or more wireless signal sets between oneor more target devices and a plurality of reference devices, saidplurality of reference devices defining a coordinate system, said one ormore target devices and at least one of the plurality of referencedevices located at unknown positions in the coordinate system, eachwireless signal set comprising at least a first-speed signal having afirst transmission speed and a second-speed signal having a secondtransmission speed, and the first transmission speed being higher thanthe second transmission speed; and calculating the position of thereference device whose position is unknown in the coordinate systembased on the distances between the plurality of reference devices; andfor each target device, determining the distance between the targetdevice and each of the plurality of reference devices based on the timedifference between the receiving time of the first-speed signal and thereceiving time of the second-speed signal of the wireless signal setcommunicated between the target and reference devices; and determiningthe position of said target device in the coordinate system based on thedetermined distances.
 13. The positioning method of claim 12 wherein thefirst-speed signal is a Radio Frequency (RF) signal, and thesecond-speed signal is an acoustic signal.
 14. The positioning system ofclaim 10 wherein the at least one processing unit is further configuredfor measuring the distances between the plurality of reference devices.15. The positioning system of claim 10 wherein said one or more wirelesssignal sets comprises a wireless signal set transmitted from one of theone or more target devices and received by the plurality of referencedevices for determining the distance between the target device and eachof the plurality of reference devices based on the time differencebetween the receiving time of the first-speed signal and the receivingtime of the second-speed signal of the wireless signal set.
 16. Thepositioning system of claim 10 wherein the distance between the targetdevice and each reference device is determined as:${d = \frac{c_{1}c_{2}\Delta\; t}{c_{1} - c_{2}}},{{\Delta\; t} = {t_{SA} + \frac{n_{0}}{F_{S}} - t_{RF}}},$wherein d is the distance between the target device and the referencedevice, Δt is the time difference between the time of receiving thefirst-speed signal and the time of receiving the second-speed signal, c₁is the first speed, c₂ is the second speed and c₁ >c₂, t_(SA) is thetime at which sampling of the acoustic signal began, F_(s), is thesampling rate of sampling the received acoustic signal, and t_(RF) isthe time-of-arrival of the first-speed signal, and n₀ is an estimatedoffset between the time-of-arrival of the acoustic signal and t_(SA).17. The positioning system of claim 10 wherein the first-speed signaland the second-speed signal of each signal set are simultaneouslytransmitted.
 18. The positioning system of claim 10 wherein at least oneof the first-speed signal and the second-speed signal is encoded. 19.The positioning system of claim 11 wherein each of at least one targetdevice and at least one reference device further comprises a temperaturesensor; and wherein the at least one processing unit is furtherconfigured for: calculating a first temperature-adjusted speed of soundat the at least one target device by using a temperature measurementobtained by the temperature sensor of the at least one target device;calculating one or more second temperature-adjusted speeds of sound atthe at least one reference device by using temperature measurementsobtained by the temperature sensor of the at least one reference device;and calculating a calibrated speed of the acoustic signal by averagingthe first and the one or more second temperature-adjusted speeds ofsound.
 20. The positioning method of claim 12 wherein said communicatingthe one or more wireless signal sets between the one or more targetdevices and the plurality of reference devices comprises: transmittingone of said wireless signal sets from one of the one or more targetdevices; and receiving said wireless signal set at the plurality ofreference devices.
 21. The positioning method of claim 13 furthercomprising: calculating a first temperature-adjusted speed of sound atthe at least one target device by using a temperature measurementobtained by the at least one target device; calculating one or moresecond temperature-adjusted speeds of sound at the at least onereference device by using temperature measurements obtained by the atleast one reference device; and calculating a calibrated speed of theacoustic signal by averaging the first and the one or more secondtemperature-adjusted speeds of sound.